Criterion for the convergence of the solution of the Riccati differential equation
- 1 December 1981
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 26 (6) , 1232-1242
- https://doi.org/10.1109/tac.1981.1102812
Abstract
The optimal control problem for a linear system with a quadratic cost function leads to the matrix Riccati differential equation. The convergence of the solution of this equation for increasing time interval is investigated as a function of the final state penalty matrix. A necessary and sufficient condition for convergence is derived for stabilizable systems, even if the output in the cost function is not detectable. An algorithm is developed to determine the limiting value of the solution, which is one of the symmetric positive semidefinite solutions of the algebraic Riccati equation. Examples for convergence and nonconvergence are given. A discussion is also included of the convergence properties of the solution of the Riccati differential equation to any real symmetric (not necessarily positive semidefinite) solution of the algebraic Riccati equation.Keywords
This publication has 13 references indexed in Scilit:
- A necessary and sufficient condition for the solution of the Riccati equation to be periodicIEEE Transactions on Automatic Control, 1980
- The asymptotic behavior of constant-coefficient Riccati differential equationsIEEE Transactions on Automatic Control, 1976
- The geometry of the riccati equationStochastics, 1975
- Matrix quadratic equationsBulletin of the Australian Mathematical Society, 1974
- Linear Multivariable ControlPublished by Springer Nature ,1974
- On nonnegative definite solutions to matrix quadratic equationsAutomatica, 1972
- On the matrix riccati equationInformation Sciences, 1971
- Least squares stationary optimal control and the algebraic Riccati equationIEEE Transactions on Automatic Control, 1971
- Stabilization controllability and observability of linear autonomous systemsIndagationes Mathematicae, 1970
- On a Matrix Riccati Equation of Stochastic ControlSIAM Journal on Control, 1968